The shortest side of a right-angled triangle is 6cm shorter than its hypotenuse. The difference in the length of the other two sides is 3cm. If the shortest side is (n-3), show that $2 n^{2} = 12 n$ . Hence find n.

Open in App

Solution

Short side be = n-
Hypotenuse = (n-3)+6=n+3
Longest side = (n-3)+6-3=n
By Pythagoras theorem,
$n^{2} + (n - 3)^{2} = (n + 3)^{2}$
$n^{2} + n^{2} - 6 n + 9 = n^{2} + 6 n + 9$
$n^{2} - 6 n = 6 n$
$n^{2} = 12 n$
n(n-12)=0
n=0 and n=12

Suggest Corrections

Similar questions

The hypotenuse of a right-angled triangle is 1 metre less than twice the shortest side. If the third side is 1 metre more than the shortest side, find the sides of the triangle.

Q. The hypotenuse of a right angled triangle is

6

metres more than twice the shortest side. If the third side is

2

metres less than the hypotenuse, find the sides of the triangle.

Q. A grassy land in the shape of a right angled triangle has its hypotenuse

1

metre more than twice the shortest side. If the third side is

7

metres more than the shortest side. The sides of the grassy land are:

Q. The sides (other than hypotenuse) of a right triangle are in the ration 3:4. A rectangle is described on its hypotenuse, the hypotenuse being the longer side of the rectangle. The breadth of the rectangle is 4/5 of its length. Find the shortest side of the right triangle if the perimeter of the rectangle is 180cm.

Q. The hypotenuse of a right triangle is

3 m

more than twice of the shortest side.
If the third side is

1 m

less than the hypotenuse. Find the shortest side?

Join BYJU'S Learning Program

The shortest side of a right-angled triangle is 6cm shorter than its hypotenuse. The difference in the length of the other two sides is 3cm. If the shortest side is (n-3), show that 2n2=12n. Hence find n.

Short side be = n- Hypotenuse = (n-3)+6=n+3 Longest side = (n-3)+6-3=n By Pythagoras theorem, n2+(n−3)2=(n+3)2 n2+n2−6n+9=n2+6n+9 n2−6n=6n n2=12n n(n-12)=0 n=0 and n=12

The shortest side of a right-angled triangle is 6cm shorter than its hypotenuse. The difference in the length of the other two sides is 3cm. If the shortest side is (n-3), show that $2 n^{2} = 12 n$ . Hence find n.

Short side be = n-
Hypotenuse = (n-3)+6=n+3
Longest side = (n-3)+6-3=n
By Pythagoras theorem,
$n^{2} + (n - 3)^{2} = (n + 3)^{2}$
$n^{2} + n^{2} - 6 n + 9 = n^{2} + 6 n + 9$
$n^{2} - 6 n = 6 n$
$n^{2} = 12 n$
n(n-12)=0
n=0 and n=12