In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM - MC = 7$ and $AB^{2} - BC^{2} = 175$,then $AC = \ldots$
- A$\sqrt{224}$
- B$\sqrt{216}$
- C$25$
- D$20$
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View SolutionWhich of the following correctly matches the information in Part $I$ and Part $II$?
Part $I$ Part $II$ $1.$ In $\Delta ABC$,$\angle B$ is a right angle and $\overline{BM}$ is a median. $a. AB^2 + BC^2 = 2(BD^2 + CD^2)$ $2.$ In $\Delta ABC$,$\angle A$ is a right angle and $\overline{AD}$ is an altitude. $b. BC = \frac{1}{2} AB$ $3.$ In $\Delta ABC$,$m\angle C = 90^\circ$ and $m\angle A = 30^\circ$. $c. AC^2 = CD \cdot BC$ $4.$ In $\Delta ABC$,$\overline{BD}$ is a median. $d. BM = \frac{1}{2} AC$
| Part $I$ | Part $II$ |
|---|---|
| $1.$ In $\Delta ABC$,$\angle B$ is a right angle and $\overline{BM}$ is a median. | $a. AB^2 + BC^2 = 2(BD^2 + CD^2)$ |
| $2.$ In $\Delta ABC$,$\angle A$ is a right angle and $\overline{AD}$ is an altitude. | $b. BC = \frac{1}{2} AB$ |
| $3.$ In $\Delta ABC$,$m\angle C = 90^\circ$ and $m\angle A = 30^\circ$. | $c. AC^2 = CD \cdot BC$ |
| $4.$ In $\Delta ABC$,$\overline{BD}$ is a median. | $d. BM = \frac{1}{2} AC$ |
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