Question

Q.10 The base of a right angle triangle is 48 cm and its hypotenuse is 50 cm. The area of the triangle is:​

Answer 1

★ Given:-  

• ➳ Base = 48 cm.
• ➳ Hypotenuse = 50 cm.

★ To find:-        

• ➛ The area of the triangle.

★ Solution:-        

Here, we have given that the base of the right angle triangle is 48 cm and its hypotenuse is 50 cm.

So firstly we will find out the perpendicular of the right angle triangle by using The Pythagoras Theorem.

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$\qquad\tt{:\implies\:\bigg(\:Base\:\bigg)^{2}\:+\:\bigg(\:Height\:\bigg)^{2}\:=\:\bigg(\:Hypotenuse\:\bigg)^{2}}$

$\qquad\tt{:\implies\:\bigg(\:48\:\bigg)^{2}\:+\:\bigg(\:Height\:\bigg)^{2}\:=\:\bigg(\:50\:\bigg)^{2}}$

$\qquad\tt{:\implies\:\bigg(\:2304\:\bigg)\:+\:\bigg(\:Height\:\bigg)^{2}\:=\:\bigg(\:2500\:\bigg)}$

$\qquad\tt{:\implies\:\bigg(\:Height\:\bigg)^{2}\:=\:\bigg(\:2500\:-\:2304\:\bigg)}$

$\qquad\tt{:\implies\:\bigg(\:Height\:\bigg)^{2}\:=\:\bigg(\:196\:\bigg)}$

$\qquad\tt{:\implies\:\bigg(\:Height\:\bigg)\:=\:\sqrt{196} }$

$\qquad\tt{:\implies\:\bigg(\:Height\:\bigg)\:=\:14\:cm}$

. ° . The height of the right angle triangle is 14 cm.

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Now we will find out the area of the triangle by using the formula.

$\qquad\tt{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\dfrac{1}{2}\:\times\:base\:\times\:height}$

$\qquad\tt{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\dfrac{1}{2}\:\times\:48\:\times\:14}$

$\qquad\tt{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\dfrac{1}{2}\:\times\:672}$

$\qquad\tt{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:\dfrac{672}{2}}$

$\qquad\tt{:\implies\:Area\:_{(\:TRIANGLE\:)}\:=\:336\:cm^{2}}$

. ° . The area of the triangle is 336 cm².

                      ___________