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scoray [572]
3 years ago
8

Please help :)

Mathematics
1 answer:
spin [16.1K]3 years ago
7 0

The ratios 84/105 and 128/160 are proportional

<u>Solution:</u>

Given, two ratios are \frac{84}{105} and \frac{128}{160}

We have to give two different reasons to support the answer.

<em><u>Reason 1:</u></em>

Now, we know that, numerators and denominators should be proportional to be two fractions in proportion.

\text { Then, } \frac{84}{128}=0.65625 \text { and } \frac{105}{160}=0.65625

So numerators and denominators are in proportion, then given two fractions are proportion.

<em><u>Reason 2:</u></em>

Now, values of two fractions must be equal:

\rightarrow \frac{84}{105}=\frac{128}{160} \rightarrow 84 \times 160=105 \times 128 \rightarrow 13440=13440

So, values of two fractions are equal, then they are in proportion.

Hence, the given two fractions are in proportion.

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Triangle rsu = Triangle tus

Statements Reasons

UR ≅ TS  Definition of Rectangle

US ≅ US Reflexive Property

<U, <T, <R, <S are all congruent and right angles

Definition of Rectangle

ΔRSU ≅ ΔTUS Side, Angle, Side

UR ≅ TS     CPCTC

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2. Pythagoras Theorem

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Triangle TUS

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UR measure / sin (60) x (90) = US measure.

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