Question
What is the length of the hypotenuse in an isosceles
right-angled triangle if one of its equal sides measures 5√3 cm?Solution
ATQ, 
ATQ, Since ΔABC is an isosceles right-angled triangle, then AC = AB ⇒ AC = AB = 5√3 cm (Given) Now, using the Pythagoras theorem, we get BC² = AC² + AB² ----(1) ⇒ BC² = AB² + AB² [Using (1)] ⇒ BC² = 2AB² ⇒ BC² = 2(5√3)² ⇒ BC² = 2(25 × 3) ⇒ BC² = 150 ⇒ BC = √150 = 5√6 cm Hence, the length of the hypotenuse is 5√6 cm.
A sum of money is invested at a rate of 5% per annum simple interest. If the interest earned in 3 years is ₹900, what is the sum of money invested?
Shivam invested 21000 at 12% p.a. simple interest for ‘x’ months. If at the end of ‘x’ months, he received a total amount of Rs.25200. What is t...
A borrowed Rs. 7000 from B for his business. How much amount A will return to B at the end of 30 months such that the sum was borrowed at simple interes...
A man deposited Rs. 9000 at 10% compound interest, compounded annually while Rs. 8500 at 13% simple interest per annum. What will be the difference betw...
A shopkeeper marked an article ‘A’ 60% above the cost price and sold it for Rs. 2016 after giving a certain discount while he sold an articl...
A certain sum of money invested at a rate of 36% p.a. amounts to Rs. 30417.5 at the end of 15 months if the rate of interest is compounded 5 monthly. Fi...
Amit took a loan of Rs. 36000 at 10% per annum simple interest for 3 years. He invested the full amount in a scheme offering 13% p.a. simple interest fo...
Rs. 90Y when invested for 5 years at simple interest of 12% p.a., yields an interest of Rs. 2700. If Rs. 110Y is invested for 3 years at compound intere...
The difference of S.I and C.I on an amount of Rs. 20000 for 2 years is Rs. 162. What is the rate of interest?
Vikas invested Rs. 12,000 at an annual compound interest rate of 30%, with the interest being compounded annually after every 10 months. What is the in...
