Question

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The area of an isosceles triangular land whose base side length 10 meters is 60 square meters. Find the measure of its remaining sides.
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Answer 1

${\large{\pmb{\sf{\underline{\dag \: \: Understanding \; the \; Question...}}}}}$

● This question says that we have to find out the measure of the remaining sides of the isosceles triangular land whose area is 60 metres sq. and the base side length is 10 meters. Let us solve this question.

${\large{\pmb{\sf{\underline{\dag \: \: Given \; that...}}}}}$

● Area of the isosceles triangular land = 60 metres sq.

● Base side length of the isosceles triangular land = 10 metres

${\large{\pmb{\sf{\underline{\dag \: \: To \; find...}}}}}$

● The measure of the remaining sides of the isosceles triangular land

${\large{\pmb{\sf{\underline{\dag \: \: Solution...}}}}}$

● The measure of the remaining sides of the isosceles triangular land = 13 metres

${\large{\pmb{\sf{\underline{\dag \: \: Using \; concepts...}}}}}$

● Formula to find out the area of a triangle.

● Phythagoras Theorm formula.

${\large{\pmb{\sf{\underline{\dag \: \: Using \; formulas...}}}}}$

$\: \: \: \: \: \: \: \: \: \sf \underset{\blue{\sf Area \: of \: triangle}}{\underbrace{\small{\boxed{\pink{\sf{\dfrac{1}{2} \times Base \times Height}}}}}}$

$\sf \underset{\blue{\sf Phythagoras \: Theorm}}{\underbrace{\small{\boxed{\pink{\sf{Hypotenuse^2 \: = Base^2 \: + Perpendicular^2}}}}}}$

${\large{\pmb{\sf{\underline{\dag \: \: Full \; Solution...}}}}}$

~ Firstly by using the formula to find out the area of triangle let us find out the base of the triangle, an! Don't be confused that base is already given, there read the question again base is not given base side length is given.

$\sf \underset{\blue{\sf Area \: of \: triangle}}{\underbrace{\small{\boxed{\pink{\sf{\dfrac{1}{2} \times Base \times Height}}}}}} \\ \\ :\implies \sf Area \: of \: traingle \: = \dfrac{1}{2} \times Base \times Height \\ \\ :\implies \sf 60 = \dfrac{1}{2} \times 10 \times Height \\ \\ :\implies \sf 60 = 5 \times Height \\ \\ :\implies \sf 60/5 \: = Height \\ \\ :\implies \sf 12 \: = Height \\ \\ :\implies \sf Height \: = 12 \: metres$

Henceforth, we get height as 12 metres. The isosceles triangular land divide it into two parts. It means 5 metres is the base of the given isosceles triangular land.

~ Now using the Phythagoras Theorm we have to find out the measure of its remaining sides.

$\sf \underset{\blue{\sf Phythagoras \: Theorm}}{\underbrace{\small{\boxed{\pink{\sf{Hypotenuse^2 \: = Base^2 \: + Perpendicular^2}}}}}} \\ \\ :\implies \sf Hypotenuse^2 \: = Base^2 \: + Perpendicular^2 \\ \\ :\implies \sf Hypotenuse^2 \: = 5^2 + 12^2 \\ \\ :\implies \sf Hypotenuse^2 \: = 25 + 144 \\ \\ :\implies \sf Hypotenuse^2 \: = 169 \\ \\ :\implies \sf Hypotenuse \: = \sqrt{169} \\ \\ :\implies \sf Hypotenuse \: = 13 \: metres$

Henceforth, hypotenuse is 13 metres. That's the measure of the remaining sides.

• Remember? That isosceles triangle is that triangle whose any two sides are equal.