Question
Download Solution PDFA triangle has two equal sides, and the third side is 1.5 times any of these sides. If the perimeter of the triangle is 14 units, then the area of the triangle is ________ square units.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Two equal sides of a triangle.
Third side is 1.5 times any of the equal sides.
Perimeter of the triangle is 14 units.
Formula Used:
Area of triangle = 1/2 × base × height
Calculation:
Let x be the length of the equal sides
and 1.5x be the length of the third side.
⇒ x + x + 1.5x = 14
⇒ 3.5x = 14
⇒ x = 14 ÷ 3.5 = 4 units
Third side = 1.5 × 4 = 6 units
Height of the triangle,
⇒ h = √(42 - (6/2)2)
⇒ √(16 - 9) = √7 units
Area of triangle = 1/2 × base × height
⇒ 0.5 × 6 × √7 = 3√7 square units.
Therefore, the area of the triangle is 3√7 square units.
Last updated on Jun 30, 2025
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