each of equal sides of an isosceles triangle is 4cm greater than its height .If the base of triangle is 24 cm ,calculate the per imeter and the area of the triangle
1 answer:
<h3>
<u>Answer</u> <u>:</u> <u>-</u> </h3>
192 cm²
<h3>
<u>Step</u> <u> </u> <u>by</u> <u> step</u> <u> explanation</u> <u> </u> <u>:</u> <u>-</u> </h3>
Let us take the height be x , then its side = x + 4. Now half of base will be 12 cm .
<u>According</u><u> to Pythagoras Theorem :- </u>
=> base² + perpendicular ² = hypontenuse ²
=> 12² + x² = (x+4)²
=> 144 + x² = x² + 16 + 8x
=> 8x = 144-16
=> 8x = 128
=> x = 128/8
= > x = 1 6 cm .
Hence the height of ∆ is 1 6 cm . So the area will be half the product of base and altitude.
= 1/2 * 16 cm * 24cm .
= 192 cm²
<h3>
<u>★</u> <u> </u> <u>Hence</u> <u> </u> <u>the</u> <u> </u> <u>area</u> <u> </u> <u>of</u> <u> </u> <u>the </u> <u>tria</u> <u>ngle</u> <u> is</u> <u> </u> <u>1</u> <u>9</u> <u>2</u> <u> </u> <u>cm²</u> <u> </u> <u>.</u> </h3>
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