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Rectangles & Circles

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1.

A rectangle has has an area of 112 cm². The length and the width of the rectangle are changed by a scale factor of 1.5.

What is the area of the new rectangle?

2.

What is the measure of  SU⏜?

3.

Circle F is intersected by HI←→ and IJ↔ and ​ m∠HIJ=101° ​

What is the measure of  HJ⏜?

Guest May 31, 2017
#1
+7324
+1

1.

area of old rectangle = L * W

area of new rectangle = (1.5) * L * (1.5) * W

area of new rectangle = 2.25 * L * W

area of new rectangle = 2.25 * area of old rectangle

area of new rectangle = 2.25 * 112 cm2

area of new rectangle = 252 cm2

2.

$$\angle{STU}=\frac12\,\cdot\,\overset{ \frown}{SU} \\~\\ 64^{\circ}=\frac12\,\cdot\,\overset{\frown}{SU} \qquad \text{ Multiply both sides of the equation by 2.} \\~\\ 128^{\circ}=\overset{\frown}{SU}$$

3.

$$m\overset{\frown}{HJ}=180^{\circ}-101^{\circ}=79^{\circ}$$

Also, I noticed the 281º in the bottom right of the circle.

$$m\overset{\frown}{HJ}=360^{\circ}-281^{\circ}=79^{\circ}$$

hectictar  May 31, 2017