5. The base and the height of a triangle are in
the ratio 4: 5. If the area of the triangle is
40 m2; find its base and height.
Let base be 4x m and height be 5x m.
2 x 4x x 5x = 40.
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✪ Question ✪
The base and the height of a triangle are in the ratio 4:5. If the area of the triangle is 40 m², find its base and height.
✪ Given ✪
- Ratio of base to height = 4:5
- Area = 40m²
✪ To find ✪
The base and height.
✪ Solution ✪
Let base be 4x m and height be 5x m.
Area of triangle = (1/2 × Base × Height) unit²
According to condition,
1/2 × 4x × 5x = 40
⇒20x²/2 = 40
⇒20x² = 40 × 2
⇒20x² = 80
⇒x² = 80/20
⇒x² = 4
⇒x = √4
⇒x = √(2×2)
⇒x = 2
✪ Hence ✪
x = 2
- Base = 4x m = (4×2) m = 8 m
- Height = 5x m = (5×2) m = 10 m
✪ Therefore ✪
Its base and height are 8 m and 10 m respectively.
๑ Hope this helps you. ๑
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