Question

Find the base of an isosceles triangles whose
area is 12cm and the length of one of the equal
side is 5 cm.​

Answer 1

⠀⠀⠀⠀⠀☛...Given...☚ ⠀⠀ ⠀

⠀Area of isosceles triangle = 12cm²

⠀The length of one side = 5cm

⠀⠀⠀⠀⠀☛...To find...☚ ⠀⠀

⠀The base length...

⠀⠀⠀⠀ ☛...Solution...☚⠀⠀

We know...

area of area of triangle = $\dfrac{1}{2}\times{base}\times{height}$

⠀Let the base be "b"...and height be "h"...

Using Pythagoras theorem to find the height...

⠀base² + height² = hypotenuse²

⠀b² + h² = 5²

So...

⠀b² + (12/b)² = 5²

__________

b × h = 12

h = 12 / h

__________

⠀b² + 144/b² = 5²

⠀144 - 25b² = 0 -------- eq 1...

So next (b + 4)(b – 4)(b + 3)(b – 3) = 0

Neglecting the negative values, b could be 3 giving h = 4

or b could be 4cm... giving h = 3cm...

This means the whole base could be 6cm... and the height is 4cm...

OR the whole base could be 8cm and the height is 3cm...⠀ ⠀ ⠀⠀ ⠀⠀⠀

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