Question

the base of an isosceles triangle is 10 cm and one of its equal sides is 13 cm find its area and length of altitude to the base

Answer 1

Answer:

Step-by-step explanation:

given: isosceles triangle with equal sides 13cm and base 10cm

to find: area and length of altitude

solution: let the base be BC. draw an altitude from point A meeting base BC at D.

so, AB=AC=13cm

in triangle ACD and triangle ABD

AB=AC (equal sides of an isosceles triangle)

AD=AD (common)

angle ADB = angle ADC =90 (altitude AD)

by RHS, triangle ACD is congruent to triangle ABD

by CPCT, BD = DC =1/2 * 10 = 5cm

in triangle ACD,

AC^2 - CD^2 = AD^2 (pythagoras theorem)

13^2 - 5^2 = AD^2

169-25 = AD^2

144 = AD^2

12cm = AD = length of altitude

now, in triangle ABC,

ar = 1/2bh

ar = 1/2*10*12

ar = 60cm^2