Question

The two legs of a right triangle are in the ratio √5/2. If the area is 9√5 square units, find the length of the hypotenuse?

Answer 1

Answer:

Step-by-step explanation:

Let the two legs be √5 x and 2x respectively. The area of the triangle is given as 9√5 sq units.

Area of a right triangle= 1/2 × product of its legs:

9√5=1/2×√5 x × 2x

√5 will get cancelled both sides and 2×1/2=1

Therefore,

9=x² which implies that x=±3. But x cannot be -3,since x is a length .

Therefore the legs of the right Δ are √5×3=3√5 units and 2×3=6 units.

Now on applying pythoguras thearm which states that: "In a right angle Δ,the square of the lenghts of the side is equal to the square of the hypotanuse"

Let the hypotenuse be h.

h²=(3√5)²+6²

h²=45+36

h²=81

∴h=±9 ,but length cannot be negative,so h=9

∴THE HYPOTENUSE IS 9 UNITS.