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The height of a triangle is 90 cm. What lengths of the base will make the area at most 500 cm2 a) {b|b≤11.1¯ cm} b) {b|b<11.1¯ cm} c) {b|b≥5.5¯ cm} d) {b|b≥11.1¯ cm}

Respuesta :

The length of the base is b ≤ 11.1 cm.

Solution:

Height of the triangle = 90 cm

Area of the triangle is at most 500 cm²

Area of the triangle ≤ 500

[tex]$\frac{1}{2}\times \text{base}\times\text{height} \leq 500[/tex]

[tex]$\frac{1}{2}\times b\times 90 \leq 500[/tex]

b × 45 ≤ 500

Divide by 45 on both sides.

[tex]$\frac{b \times 45}{45}\leq \frac{500}{45}[/tex]

b ≤ 11.11111111 cm

b ≤ 11.1 cm

The length of the base is b ≤ 11.1 cm.

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