Formula for the rectangle area is a * b, In this case we know that:

a * b = 180
a (width) = unknown
b (length) = 1 1/4a

We can write it down as:

a * 1 1/4 * a = 180
a² * 1 1/4 = 180 / ÷ 1 1/4 (both sides)
a² = 144 / square root (both sides)
a = 12

Doublecheck:

a = 12
b = 1 1/4 * 12 = 15
a * b = 12 * 15 = 180 (so it's correct)

Answer: The dimensions of the painting are <u>12 x 15 inches</u>.

8 0

3 years ago

Hi, does anyone know how to solve this. If so, please show the working out too. Thanks.

sergiy2304 [10]

See the explanation

<h2>Explanation:</h2><h2 />

I have corrected your diagram so ∅ is the angle at the top of the diagram. In order to solve this problem we have to use Pythagorean theorem and the law of sines. Moreover, I have named two sides as w and z so those variables will help us to solve this problem. So:

The triangle at the bottom is right, so by Pythagorean theorem is true that:

$w^2=4^2+(2\sqrt{2})^2 \\ \\ w^2=24 \\ \\ w=\sqrt{24} \\ \\ w=2\sqrt{6}$

By law of sines:

$\frac{z}{sin\theta}=\frac{w}{sin60^{\circ}} \\ \\ z=\frac{wsin\theta}{sin60^{\circ}} \\ \\ z=\frac{2\sqrt{6}sin\theta}{\sqrt{3}/2} \\ \\ z=4\sqrt{2}sin\theta$

By law of sines again:

$\frac{y}{sin45^{\circ}}=\frac{z}{sin\phi} \\ \\ y=\frac{zsin45^{\circ}}{sin\phi} \\ \\ y=\frac{4\sqrt{2}sin\theta \sqrt{2}/2}{sin\phi} \\ \\ \\ Finally: \\ \\ \boxed{y=\frac{4sin\theta}{sin\phi}}$

<h2>Learn more:</h2>

Classification of triangles: brainly.com/question/10379190

#LearnWithBrainly

7 0

3 years ago