Question

(ii) Find the base of an isosceles triangle whose area is 60 sq.cm and length of equal sides is 13 cm

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Answer 1

if the height is h and the base is 2b

then we have:

½(2bh)=60→2bh=120

b²+h²=13²=169

so

(b+h)²=b²+h²+2bh=120+169=289

(b-h)²=b²+h²-2bh=169-120=49

so

b+h=17

|b-h|=7

so b can be 12 and h can be 5

or b can be 5 and h can be 12

which means the base is either 24cm or 10cm