Question

area of an isoscels right triangle is 32 find the length of the altitude drawn from the longest side

Answer 1

The area of any triangle is half the product of base and height. An isosceles right triangle is one where a right angle is present and the base and perpendicular are equal. So in this case, area can be written as half of the base squared.

0.5 base² = 32

base² = 64

base = 8

Lengths are always positive hence base is 8 units.

Now in an isosceles triangle the altitude to the non-equal side bisects this side.

Hence, in your triangle, the longest side hypotenuse is bisected by the altitude.

In isosceles right triangle hypotenuse is √2 times the base.

Hence bisection makes each part √2/2 times base of the hypotenuse.

Half of hypotenuse = 8√2/2 = 4√2

applying pythagoras theorem in triangle formed by altitude.

base² + perpendicular² = hypo²

(4√2)²+ p² = 8²

p² = 64-32

p² = 32

p = 4√2

Hence the length of altitude is 4√2 unit

Answer 2

Let the triangle be named ABC
area of a triangle is 1/2b×h=32
B×H=32×2/1
B×H=64

we know that triangle is an isosceles triangle
so,b=h
so,√64=b=h
8=b=h

Now coming to the hypotenuse
we know h=AB^2+BC^2
So,8^2+8^2=h^2
64+64=h^2
128=h^2
√128=h
11.31=h

draw the triangle ABC with the measurements
then take a protractor and draw a line perpendicular to AC passing through angle b
then measure the line From AC till angle b


Ans=5.6