3 years ago

Four feet are cut from a 12-foot board. What is the percent decrease in length?

Mathematics

1 answer:

Lilit [14]3 years ago

8 0

25% is the precent decease

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Slav-nsk [51]

Given:

Area and altitude PS of ∆PQR are ar(∆PQR) = 180cm² and PS = 15.

To find:

The measure of side QR.

Solution:

According to the given information, PS is an altitude of ∆PQR. It means QR is the base of ∆PQR.

We know that, the area of a triangle is

$Area=\dfrac{1}{2}\times Base\times Height$

$ar(\Delta PQR)=\dfrac{1}{2}\times QR\times PS$

Substituting the given values, we get

$180=\dfrac{1}{2}\times QR\times 15$

$180\times 2=QR\times 15$

$360=QR\times 15$

Divide both sides by 15.

$\dfrac{360}{15}=QR$

$24=QR$

Therefore, the measure of side QR is 24 cm.

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vampirchik [111]

Given:

The figure of a right triangle.

To find:

The length of AB.

Solution:

In a right angle triangle,

$\cos \theta=\dfrac{Base}{Hypotenuse}$

Using this trigonometric ratio for the given triangle, we get

$\cos A=\dfrac{AB}{AC}$

$\cos (60^\circ)=\dfrac{AB}{10}$

$\dfrac{1}{2}=\dfrac{AB}{10}$

$\dfrac{1}{2}\times 10=AB$

$5=AB$

Therefore, the length of AB is 5 units.

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