Answer the following mathematical problems:

The hypotenuse of a right angled triangle is 2x - 6 and the other two sides are x + 2 and x. Find the value of x.

Created: 3 months ago | Updated: 3 months ago

Job Solution Combined Bank (সমন্বিত ব্যাংক) Combined 7 Banks & Financial Institutions || Senior Officer (19-11-2021) || 2021 গণিত

Add Description

$L e t, A B C i s t h e r i g h t a n g l e t r i a n g l e$

$H e r e, H y p o t e n u s e A B = (2 x - 6)$

$O n e a r m, A C = x A n d a n o t h e r a r m, B C = (x + 2) ∴ A c c o r d i n g t o P e t h a g o r e a n T h e o r e m, {(2 x - 6)}^{2} = {(x + 2)}^{2} + x^{2}$

$= {(2 x)}^{2} - 2 \times 2 x \times 6 + 6^{2} = x^{2} + 2 \times x \times 2 + 2^{2} + x^{2}$

$= 4 x^{2} - 24 x + 36 = 2 x^{2} + 4 x + 4 = 2 x^{2} - 28 x + 32 = 0 = x^{2} - 14 x + 16 = 0$

$N o w, c o m p a r i n g, x^{2} - 14 x + 16 = 0 w i t h a x^{2} + b x + c = 0, W e g e t, x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} = \frac{- (- 14) \pm \sqrt{{(- 14)}^{2} - 4 \times 1 \times 16}}{2 \times 1} = \frac{14 \pm \sqrt{196 - 64}}{2} = \frac{14 \pm \sqrt{132}}{2} = \frac{14 \pm \sqrt{4 \times 33}}{2}$

$= \frac{14 \pm 2 \sqrt{33}}{2} = \frac{2 (7 \pm \sqrt{33})}{2} = 7 \pm \sqrt{33} ∴ x = (7 + \sqrt{33}) o r (7 - \sqrt{33})$

3 months ago

0 0

স্বপ্নদর্শী

Verified

A man engaged a worker on the condition that he would pay him Tk.30,000 and one uniform after one year of service. The worker served only 9 months and got Tk 22,000 and a uniform. What is the price of the uniform?

Created: 3 months ago | Updated: 3 months ago

Job Solution Combined Bank (সমন্বিত ব্যাংক) সমন্বিত ব্যাংক ।। অফিসার জেনারেল (31-03-2023) || 2023 গণিত

224

Add Description

Solve the following problems:

The price of 3 horses is same as the cost of 5 cows. If total cost of 4 horses and 6 cows is Tk 1900, find the cost of one horse.

Created: 3 months ago | Updated: 3 months ago

Job Solution Combined Bank (সমন্বিত ব্যাংক) সমন্বিত ব্যাংক ।। অফিসার জেনারেল (31-03-2023) || 2023 গণিত

237

Add Description

Solve the following problems:

A man won a lottery of Tk.20,00,000. He gave 2/5 of the amount to his wife and 1/4 of the balance to his son. He donated 2/9 of the balance amount. How much money was donated?

Created: 3 months ago | Updated: 3 months ago

Job Solution Combined Bank (সমন্বিত ব্যাংক) সমন্বিত ব্যাংক ।। অফিসার জেনারেল (31-03-2023) || 2023 গণিত

251

Add Description

Solve the following problems:

Reena took loan of Tk 1200 at simple interest rate for as many years as the rate of interest. If she paid Tk.432 as interest at the end of the loan period, what is the rate of interest?

Created: 3 months ago | Updated: 3 months ago

Job Solution Combined Bank (সমন্বিত ব্যাংক) সমন্বিত ব্যাংক ।। অফিসার জেনারেল (31-03-2023) || 2023 গণিত

270

Add Description

Solve the following problems:

A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 12√2 cm, then what is the area of the triangle?

Created: 3 months ago | Updated: 3 months ago

Job Solution Combined Bank (সমন্বিত ব্যাংক) সমন্বিত ব্যাংক ।। অফিসার জেনারেল (31-03-2023) || 2023 গণিত

268

Add Description

Answer the following mathematical problems:

The hypotenuse of a right angled triangle is 2x - 6 and the other two sides are x + 2 and x. Find the value of x.

Related Questions

Solve the following problems:

A man engaged a worker on the condition that he would pay him Tk.30,000 and one uniform after one year of service. The worker served only 9 months and got Tk 22,000 and a uniform. What is the price of the uniform?

Solve the following problems:

The price of 3 horses is same as the cost of 5 cows. If total cost of 4 horses and 6 cows is Tk 1900, find the cost of one horse.

Solve the following problems:

A man won a lottery of Tk.20,00,000. He gave 2/5 of the amount to his wife and 1/4 of the balance to his son. He donated 2/9 of the balance amount. How much money was donated?

Solve the following problems:

Reena took loan of Tk 1200 at simple interest rate for as many years as the rate of interest. If she paid Tk.432 as interest at the end of the loan period, what is the rate of interest?

Solve the following problems:

A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 12√2 cm, then what is the area of the triangle?