Question

A right triangle ABC is shown below: A right triangle ABC with height AB labeled 2 units and base BC labeled 5 units is shown. The area of the triangle above will equal one-half of a rectangle that is 5 units long and __ units wide. (Input only whole numbers, such as 8) Numerical Answers Expected!

Answer 1

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$\underline{\underline{\bf {Given}}}\begin{cases} & \sf{\bullet\:Ar_{(Triangle)}\:=\:\dfrac{1}{2}\:\times\:Ar_{(Rectangle)}} \\ & \sf{\bullet\:Height_{(Triangle)}\; = \:\bf{2\;units}}\\ & \sf{\bullet\:Base_{(Triangle)}\:=\:\bf{5\:units}}\\ & \sf{\bullet\:Length_{(Rectangle)}\:=\:\bf{5\:units}}\: \end{cases}$

$\underline{\underline{\bf {To\:find\: :}}}$

$\qquad\qquad\:\:\:\:\:\:\sf \bullet \:Width_{(Rectangle)}\:=\:?$

$\underline{\underline{\bf {Solution\: :}}}$

$\qquad \qquad\tiny \dag \: {\underline{\frak{As\:we\;know\;that\::}}}$

$:\implies \sf \:Ar_{(Triangle)}\:=\:\dfrac{1}{2}\:\times\:Ar_{(Rectangle)}$

$:\implies \sf \dfrac{1}{2}\:\times\:Base\:\times\:Height\:=\:\dfrac{1}{2}\:\times\:Length\:\times\:Width$

$:\implies \sf \cancel{\dfrac{1}{2}}\:\times\:Base\:\times\:Height\:=\:\cancel{\dfrac{1}{2}}\:\times\:Length\:\times\:Width$

$:\implies \sf Base\:\times\:Height\:=\:Length\:\times\:Width$

$:\implies \sf 5\:\times\:2\:=\:5\:\times\:Width$

$:\implies \sf \cancel{5}\:\times\:2\:=\:\cancel{5}\:\times\:Width$

$:\implies \sf Width\:=\:2$

$\underline{\boxed{\sf{\therefore\:Width_{(Rectangle)}\:=\:\bf{2\:units}}}}$

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