If the sides of a right-angled triangle are i | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the sides of the right-angled triangle be $a - d, a, a + d$ where $d > 0$.Since it is a right-angled triangle,the square of the hypotenuse is

Vedclass · Accepted Answer

$3:4:5$

Vedclass · Answer

(C) Let the sides of the right-angled triangle be $a - d, a, a + d$ where $d > 0$.Since it is a right-angled triangle,the square of the hypotenuse is equal to the sum of the squares of the other two sides:$(a - d)^2 + a^2 = (a + d)^2$$a^2 + d^2 - 2ad + a^2 = a^2 + d^2 + 2ad$$a^2 = 4ad$Since $a$ is a side length $(a 
eq 0)$,we have $a = 4d$.Substituting $a = 4d$ into the sides,we get:$4d - d, 4d, 4d + d = 3d, 4d, 5d$.The ratio of the sides is $3d : 4d : 5d$,which simplifies to $3 : 4 : 5$.

If the sides of a right-angled triangle are in $A.P.$,then their ratio is:

Similar Questions

$A$ man saves $200$ rupees in each of the first three months of his job. In the subsequent months,his savings increase by $40$ rupees compared to the previous month. After how many months from the start of the job will his total savings be $11040$ rupees?

If the sum of three numbers in an $A.P.$ is $24$ and their product is $440,$ find the numbers.

Consider an $A.P.$ of positive integers,whose sum of the first three terms is $54$ and the sum of the first twenty terms lies between $1600$ and $1800$. Then its $11^{\text{th}}$ term is:

If $a, b, c$ are in $A.P.$,then $\frac{(a - c)^2}{(b^2 - ac)} = $

$A$ farmer buys a used tractor for $Rs. 12000$. He pays $Rs. 6000$ cash and agrees to pay the balance in annual instalments of $Rs. 500$ plus $12\%$ interest on the unpaid amount. How much will the tractor cost him?

Vedclass Test Series

Exam Paper Generator

Online Exam Module