A right triangle has a perimeter of 24 cm and hypotenuse of 10 cm. The lengths of the longer and shorter arms of the triangle are and respectively.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct options are
A 8
B 6
Given that the perimeter of the right-triangle is 24 cm.
If $x$ an $y$ are the longer and shorter arms of the triangle respectively, then
$x + y + 10 = 24.$
$⟹ y = 14 - x$
Using Pythagoras' theorem, we have
$x^{2} + y^{2} = 10^{2} .$
i.e., $x^{2} + (14 - x)^{2} = 100$
$⟹ x^{2} + x^{2} + 196 - 28 x = 100$
$⟹ 2 x^{2} - 28 x + 96 = 0$
$⟹ x^{2} - 14 x + 48 = 0$
$⟹ x^{2} - 8 x - 6 x + 48 = 0$
$⟹ x (x - 8) - 6 (x - 8) = 0$
$⟹ (x - 8) (x - 6) = 0$
$⟹ x = 8 and 6$
If $x = 8,$ then $y = 14 - x = 14 - 8 = 6.$
If $x = 6,$ then $y = 14 - x = 14 - 6 = 8.$
Since $x > y,$ we must have $x = 8$ and $y = 6.$
$∴$ The longer and shorter sides of the triangle are 8 cm and 6 cm respectively.

Suggest Corrections

Similar questions

Q. The perimeter of a right triangle is

24 c m

. If its hypotenuse is

10 c m

, find its area.

The perimeter of a right triangle is 24 centimeters. Three times the length of the longer leg minus two times the length of the shorter leg exceeds the hypotenuse by 2 centimeters. What are the lengths of all three sides?

Q. A right angled triangle has perimeter of length

7

and hypotenuse of length

3

. If

θ

is the largest non-right angle in the triangle, then the value of

cos θ

equals

Find the perpendicular distance of a right triangle's hypotenuse from its opposite vertex if the base and attitude of the triangle is 24 cm and 10 cm respectively.

Q. The hypotenuse of a right triangle is 10cm and radius of thE inscribed circle is 1 cm. The perimeter of the triangle is:

Join BYJU'S Learning Program